Question

consideration is being given to forming a super ten basketball conference. the top 10 university basketball teams in the country, based on past records, would be members of the super ten conference. each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. how many games would the conference commissioner have to schedule each year? (remember, mcmaster versus alberta is the same as alberta versus mcmaster.)
a. 125
b. 14
c. 45
d. 50

Explanation:

Step1: Identify combination formula

This is a combination problem where we select 2 teams out of 10, since the order of the game does not matter. The combination formula is:
$$C(n,k)=\frac{n!}{k!(n-k)!}$$
where $n=10$ (total teams) and $k=2$ (teams per game).

Step2: Substitute values into formula

$$C(10,2)=\frac{10!}{2!(10-2)!}=\frac{10\times9\times8!}{2\times1\times8!}$$

Step3: Simplify the expression

Cancel out $8!$ in numerator and denominator:
$$\frac{10\times9}{2\times1}=\frac{90}{2}=45$$

Answer:

c. 45